Thermal Analysis of Polymeric Materials

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CO (CH2 )4CO ; and B is NH (CH2 )6NH ] (see Fig. 1.18) . Naturally, nylon 6,6 could also be broken into even more blocks, namely to (CD4CED6E)n, with each of the letter representing a different chain atom. As the component segments get sufficiently long, one can expect phase separation. Since the segments are part of the polymer backbone, the typical macromolecular properties are anticipated.

The melting temperatures of the polyureas and polyamides in Figure 7.65 look like parts of a phase diagram of polyethylene, interrupted regularly by urea and amide groups. In the crystal, interruption of longer sequences of identical groups with molecular structures of different polarity or geometry can lead to nanophase separation as is illustrated in Figs. 2.106 and 5.135, discussed in the formation of mesophases in Sects. 2.5.3 and 5.5.2. The distinct odd-even difference in the melting temperatures is linked to the changes in packing and entropy with odd and even-numbered (CH2 )x- sequences, as is illustrated by the schematics \/\/ and \/\/\ for three and four CH2- groups (see also Fig. 5.123 and 5.147). The small polar groups will become threedimensionally disordered on melting due to the random coil formation of the backbone

Fig. 7.65

chain, but the chains stay in sequence along the chain. Even in the melt can the polar interaction and hydrogen bonds give a sufficient driving force for aggregation (phase separation) which may ultimately lead to the formation of amphiphilic liquid crystals, as discussed in Sect. 7.1.6. The bottom-half of Fig. 7.65 adds a number of regular copolymers that show a minimum in melting temperature at short CH2-sequence length. Both groups of polymers ultimately approach the polyethylene melting temperature. The higher melting polymers, however, may have also a shallow minimum before approaching the polyethylene values. Furthermore, this diagram is drawn on the basis of irreversible melting temperatures. The further extension to larger values of x is shown in Fig. 7.66.

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Fig. 7.66

The almost 30 examples of phase diagrams of this section show that equilibrium is rare in copolymers. Nanophase separation is found frequently when partial crystallization occurs. Dissolutions are possible by randomizing the conformations and by chemical reaction.

7.3. Glass Transitions of Copolymers, Solutions, and Blends

The change of the heat capacity and free enthalpy during the glass transition are discussed in Sect. 2.5.6 (see Figs. 2.117 and 2.118, respectively). In Chap. 4, the different methods of thermal analysis sensitive to the glass transition are described. One-component systems are then examined in Sect. 6.1.3, using the hole model to analyze the enthalpy relaxation. Also discussed are the effects of small phase-size and the presence of a strongly coupled second phase that may produce a rigid amorphous fraction. Section 6.3, finally, contains a detailed examination of several onecomponent systems. In this Sect. 7.3, a review of the glass transition of multiple component systems of copolymers, solutions, and blends is presented.

The main issues in describing polymeric materials are decoupling of chain segments and nanophase morphology (see Sects. 6.2 and 7.2). The hole theory in Sects. 6.1 and 6.3 allow the estimation of a hole volume. It is about 1/5 of the “mobile bead” volume which determines the Cp at Tg (see Figs. 2.103 and 2.117). Assuming the affected mobile units in the first surrounding sphere of the hole as four, and about 16 in the second, leads to a volume of about 20 “beads” being affected by a hole. For polystyrene, this is a volume of about 1.66 nm3, or a sphere of a radius of 0.6 nm (two beads per repeating unit, 104.2 Da, density = 1.04 Mg m 3). The glass transition is thus an ideal tool to check the properties of a nanophase structure.

760 7 Multiple Component Materials

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1,4-butadiene). Wood’s equation, listed in the figure, empirically describes such concentration dependence with a single, empirical fitting parameter, k.

Another example of the glass transitions of copolymers is given by brominated poly(oxy-2,6-dimethyl-1,4-phenylene) in Fig. 7.68. In this case the backbone structure and distribution of molecular lengths are the same for all copolymer samples. The first bromine introduced into the phenylene group adds in the meta position relative to the methyl group and deactivates the second meta position, so that only one bromine adds per phenylene [29]. The glass transition of the copolymers moves smoothly from that of one homopolymer to the other. The value of Cp at Tg decreases with the amount of bromination, an indication of stiffening of the backbone which accelerates at high bromine fractions. Note that there is no significant change in the breadth of the glass transition region with composition.

Fig. 7.68

Turning to polymer solutions, an identical equation to Wood’s equation is the Gordon-Taylor equation, as written in Fig. 7.69 (W1 M1, 1 M2 = M1, etc.). This equation was proposed to account for the glass transition in case of volume-additivity of the homopolymers. If this condition holds, the constant k should be 1 2/ 2 1, where represents the densities and the the change in expansivity at the glass transition of the homopolymers.

Assuming the conformational entropy is responsible for the glass transition, one can write the change of the glass transition temperature as a function of the fractions of flexible bonds, B, as is given in the Gibbs-Di Marzio equation. This equation can be connected to the Gordon-Taylor equation by linking the constants in the two equations. The Gordon-Taylor equation is recovered from the Gibbs-Di Marzio equation if k assumes the value 2w1/ 1w2, where the is the number of flexible bonds in the respective components, and w, the mass, both per mole of repeating units.

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Fig. 7.69

A different equation results if one assumes that the product of the change in expansivity with the glass transition temperature, Tg, is a constant, known as the empirical Simha-Boyer rule Tg = 0.113. The well-known and simple Fox expression for the glass transition temperature results on insertion of the Simha-Boyer rule into the Gordon-Taylor equation. The Gibbs-Di Marzio and the Fox equations are easily generalized to SVT or pVT equations of state when assuming that the solution can be based on simple additivity of the homopolymer properties.

To add effects of specific interactions, the Gordon-Taylor expression can be expanded into a virial expression, as in the Schneider equation, listed in Fig. 7.69 [30]. The variable W2c is the expansivity-corrected mass fraction of the Gordon-Taylor expression: W2c = kW2 / (W1 + kW2). The Schneider equation can be fitted with help of the constants K1 and K2 to many polymer/polymer solutions, as is illustrated in Sect. 7.3.2. The parameter K1 depends mainly on differences in interaction energy between the binary contacts of the components: A-A, B-B, and A-B, while K2 accounts for effects of the rearrangements in the neighborhood of the contacts.

While these equations are often used indiscriminately for homopolymer solutions and for copolymers, it can be shown that sequence distributions of copolymers, given by the reactivity ratios r1 and r2 of Sect. 3.4.1, can affect the glass transition. Different chain stiffness can result for other reactivity ratios at the same overall concentration.

In Fig. 7.70 the Barton equation for copolymer glass transitions is listed. It is based on the assumption that the four possible dyads in a copolymer, poly(A-co-B),

have the following glass transitions: AA (Tg = TgAA), BB (Tg = TgBB), AB, and BA (Tg = TgAB = TgBA). Inserting these three different glass transitions into the Gibbs-

Di Marzio equation for the intermolecular effects, leads to:

Tg = mAATgAA + mBBTgBB + 2mABTgAB ,

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Fig. 7.70

where the mi,j represent the appropriate mole fractions [31]. Similarly, the Fox equation can be used as base to describe intermolecular effects. The resulting equation is written in terms of the inverse of the glass transition and is called the Johnston equation.

The reactivity ratios for a copolymer poly(A-co-B) can be written as rA = kAA/kAB where kAA and kAB are the rate constants of the chain terminating in A continuing with another A or B unit, respectively (see Figs. 3.45 and 3.46). Out of these reactivity ratios one can calculate the run number, R, which is defined as the average number of consecutive A- and B-sequences per 100 chain units:

R = 400mAmB/[1 + {1 + 4mAmB(rArB 1)}½].

For a homopolymer, this number is zero (no run is completed). For an alternating copolymer, poly(A-alt-B), R = 100. Each run is linked by an A-B or B-A dyad, with the dyads being equal to each other, i.e., one writes: R = 100(mAB + mBA) and mAA = mA mAB = mA (R/200). The Barton equation in terms of the run number is shown in Fig. 7.70, The curve is drawn with data derived for R for poly(acrylonitrile- co-1,4-butadiene) with a value of rArB = 0.054. The run number is symmetrical to mA = 0.5, with a maximum run number R* = 81.8 [31].

Figure 7.71 illustrates the change of the glass transition for poly(styrene-co- acrylonitrile) as a function of the run number, defined in Fig. 7.70. The branches of the Barton equation (mA > mB, and mA < mB) are symmetric to the line which extends to the alternating copolymer. This treatment of Tg can also be applied to triads, and one can use the other equations of Fig. 7.69 as base, but with an increase in complexity. Stereo-specific copolymers consisting of meso and racemic dyads can be treated if the samples of different tacticity have different glass transitions [32].

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Fig. 7.71

7.3.2. Glass Transitions of Solutions

Solutions of flexible, linear macromolecules are thermodynamically described by the Flory-Huggins equation of Sect. 7.1.2. The glass transition intervenes at low temperatures by terminating the equilibrium phase diagram. Once the temperature decreases below the glass transition, phase changes, such as crystallization or liquidliquid phase separation, are frozen. The glassy system is then a solid and can exhibit sufficiently large-amplitude motion for phase transitions only in special cases.

Figure 7.72 illustrates a large number of glass transition data of polymer solutions with comparisons to the Gibbs-DiMarzio ( DM), Fox (F), and Schneider (S) equations described in Fig. 7.69 [30]. The upper left displays two sets of literature data on poly(vinylidene fluoride) poly(methyl methacrylate) solutions ( , ). The glass transition shows a positive deviation from simple additivity of the properties of the pure components, which can only be represented with the help of the indicated interaction parameters of the Schneider equation. The lower left set of data illustrates poly(oxyethylene) poly(methyl methacrylate) solutions ( , ). They are well described by all three of the equations, indicating rather small specific interactions and great similarity between volume and entropy descriptions.

The upper right curves in Fig. 7.72 display data of solutions of two aliphatic polyesters with polyepichlorohydrin. A large K2 is needed in S to account for the negative deviation of the solution with poly(butylene adipate), PBA, while the solutions with poly(ethylene adipate), PEA, show little redistribution in the contact neighborhood (K2 0). The lower right curves demonstrate that solutions of poly(vinyl chloride) and poly( -caprolactone) can be fitted with all equations. The rather large K1 and K2 must cancel, since K1 = K2 = 0 leads to the Gordon-Taylor

764 7 Multiple Component Materials

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Fig. 7.72

equation. This overview of the five polymer pairs shows that volume additivity (Gordon-Taylor equation) and additivity of flexible bonds (Gibbs-Di Marzio equation) are not sufficient to describe all polymer solutions. Specific interactions must be considered. Unfortunately, the Schneider equation accounts for the interactions only with empirical constants. The broadening of the glass transition in Fig. 7.73 indicates that mixing of polymer chains may cause additional effects.

A series of thermal-analysis traces of solutions of polystyrene of 37,000 molar mass in poly( -methylstyrene) of molar mass 90,000 is shown in Fig. 7.73 [33]. The two pure polymers show a small amount of enthalpy relaxation. The three solutions indicate a considerable broadening of the glass transition region, in contrast to the practically constant broadness with concentration in copolymers (see Fig. 7.68). Solutions of polymers are commonly characterized by such a broadened glasstransition region. The same is also seen for solutions of polymers with small molecules, such as plasticizers. The homopolymers in Fig. 7.73 display a T2 T1 of about 7 K and a Te Tb of 30 K, with the temperatures defined in Fig. 2.117, while the 50/50 solution reaches 33 and 75 K, respectively. As outlined in Sect. 7.3.1, this broadening is most likely connected with an incomplete mixing of the homopolymer sequences along the chain. It may be possible to describe this inhomogeneity as a nanophase separation of regions with nonrandom chain segments.

Plotting the glass transition temperatures of Fig. 7.73 as a function of concentration, yields Fig. 7.74. Only the Gordon-Taylor equation with a fitted constant represents the data. Similarly it is possible to fit with the Schneider equation with its two constants. Two additional equations, not in Fig. 7.69, are compared in Fig. 7.74 to the data; one, is the Couchman equation, based on additivity of the products of Cp with the logarithm of Tg, the other uses a molar additivity of the logarithn of Tg. All equations without adjustable parameters do not fit the experimental data ( ).

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Fig. 7.73

Fig. 7.74

The next figure illustrates partial solubility of the same polymers as in Figs. 7.73 and 74 by increasing the molar mass of the polystyrene. Figure 7.75 represents DSC curves of a 50/50 blends with the high molar mass poly( -methylstyrene). For the low molar mass two glass transitions are seen, but not with values of Cp that correspond to a complete phase separation. In addition, the high-temperature glass transition of the poly( -methylstyrene) is considerably broadened compared to the homopolymer

766 7 Multiple Component Materials

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Fig. 7.75

in Fig. 7.73 [33]. The straight-forward interpretation is that some, but not all of the low-molar-mass polystyrene is dissolved in the poly( -methylstyrene). The solubility can be reduced by increasing the molar mass of the polystyrene component. The higher glass transition is then much sharper and approaches the proper Cp. With even higher molar mass, one can reach complete immiscibility, as shown.

7.3.3. Glass Transitions of Copolymers

While for solutions of homopolymers the mixing of the chain segments may be incomplete when compared to the intermolecular mixing, the distribution of the chain segments of the copolymers are fixed by the polymerization reaction, as described in Sect. 3.4, i.e., the same concentration can yield different segment distributions and glass transitions. The change of the glass transition with composition and randomness of the repeating units along the chain is demonstrated in Fig. 7.71 for poly(styrene-co- acrylonitrile) based on the Barton equation. Two further examples are given in Figs. 7.76 and 7.77 for poly(acrylonitrile-co-1,4-butadiene) and poly(styrene-co- methyl methacrylate) [34], respectively. As expected, the average Tg of the two homopolymers, the Tg for the critical run number R* (= 81.8, see Fig. 7.70), and the alternating copolymers (R = 100) lie on a straight line. The usually inaccessible region between the alternating copolymer and the value for R* was achieved with special control of the sequence regularity. The data in Fig. 7.77 exhibit a minimum in Tg at an R-value of 65.2, corresponding to a styrene mole fraction of 0.57.

Special complications arise when the stereospecific homopolymers show different glass transitions for isotactic (I), syndiotactic (S), and heterotactic (H) chains. An example is the poly(methyl methacrylate). The isoand syndiotactic stereoisomers of PMMA have glass transition temperatures of 315 and 400 K, respectively. Treating the stereoisomers as copolymers with a modified Barton equation of Fig. 7.70: